This comment of Dan’s started my thinking (he’s good at that, isn’t he?).
One of the most surprising, reoccurring events this year was my constant battle with my students’ attitudes toward math. Not so much that they dislike math– the fact that they believe they can’t do it. Not that it is difficult. Not that they have to work at it. So many firmly believe they can’t do math.
I’m not sure from where they got those messages. I’m not sure how they internalized them. But they have.
I had many a conversation outside of class with individual students about this problem. It usually went something like this.
Me: What do you mean, I’ve seen you “do math”?
Student: Well, I’m fine when we’re doing the problems in class or if I’m at home. I just can’t take math tests.
Me: Huh. Well what do you say to yourself when a math test is put in front of you?
I usually got some variation on the following:
Student: I’m gonna fail… I’m no good at math… I can’t do this… I always screw up.
Me: Huh… what do you say to yourself before a game/performance/show/English test/whatever it is they’re good at?
Then we’d work on changing their thinking. We’d come up with some replacement messages and ways to integrate that into their belief systems.
Did it work? For those that took it seriously it did. Now that I think about it, it was mostly the seniors who had this entrenched negative belief system. I wish I had talked about it more in class with them. I mean, really, what’s the point of learning a new lesson if they are sitting there telling themselves they can’t do it?
Interestingly, I didn’t get this from too many of the freshmen. I need to take another look at the end of the year surveys now that school has been out for a whole week.
Do your students come to you with the same beliefs? If so, what do you do to try and change them?
Continuities 
This year I designed and taught a new module in our Business School. I had exactly the same problem as you – except that at the start of the semester I asked the first years if they thought they were no good at maths. (we’re in the UK, hence the spelling) Quite a number of hands went up. I then said that I’d like to prove them wrong. To be fair not many of them believed me – but they will as I’ve just finished marking their end of semester exams and coursework. And the pass rate is very pleasing. Not miraculous, just very pleasing. Some of the pass marks are exceptionally good. My challenge was accompanied, of course, by a shedload of help and assistance, and I did ask them to believe me and work with me. Those that did have the rewards. My approach was fairly radical and to some extent experimental, and required a great deal of energy in teaching them.
So next year I’m going to challenge that cohort again – and ask them to believe in me.
I think that we have to take it as read they they believe that they’re bad at maths, and work from there. Why they have this ingrained belief that maths is too difficult for them exists on both side of the Atlantic, as is obvious from your post. I know problems of this nature also exist in Australia. But it’s not ingrained in China, India or other emerging economies. Wonder why?
Jackie (and John)
I have thought a lot about this issue over the years. I can assure you that the feeling of ‘I suck at math’ certainly exists in Australia (I come from there) and it may surprise you to know how prevalent it is here in Singapore (where I now live and where they top international competitions in mathematics all the time).
The trigger for John’s class (I suspect) was that he communicated that he cared how they felt. This is actually quite rare in many math classes, where the only important thing seems to be doing the algebra correctly and passing. There is rarely any context given (why we are doing it is fundamental to whether we might enjoy it or not), and rarely is there any “I believe in you” message.
Where does the feeling come from? One place could be from parents (or older siblings), when they say things like “I couldn’t do that stuff in school and I still can’t do it. And it hasn’t done me any harm. Most of it is useless anyway.” Then when you add the fact that a lot of math is hard (because it is conceptual and students are still concrete), the die is cast.
Jackie’s point is spot on:
I wish I had talked about it more in class with them. I mean, really, what’s the point of learning a new lesson if they are sitting there telling themselves they can’t do it?
What’s the point, indeed?
I had a few students this year who were victims of this feeling too:
Student: Well, I’m fine when we’re doing the problems in class or if I’m at home. I just can’t take math tests.
Math confidence is a huge thing weighing a bunch of kids I taught last year down. And besides encouragement and lots of extra help, I was at a loss. But nearing the end of the year, I had this long discussion with one of my students regarding her study habits — from start to finish. I’m talking homework, studying for tests, review class notes, everything. And one thing became readily apparent, and I think this is true for more than just her.
When she was doing her homework at home, she got it because she was using the book, her class notes, and examples to guide her. Which is fine and dandy. But I realized that she had never attempted to do a problem without the book or notes or anything on her own, WITHOUT any crutches. So she would get to a test and freak out because she didn’t have some reference telling her “oh yeah, that’s the first step… you’re doing it right… keep on going…” That is what the book/notes/examples provided her.
So my suggestion to her, perhaps a little too little and a little too late, was to leave certain homework problems undone, go do some other class’s assignment, and then come back work on those undone problems without looking at anything. It’s “just” homework, so she wasn’t going to be graded if she didn’t get it. And that way she could test to see if she had complete understanding of the topic or only partial understanding. She could also see precisely where she messed up. So instead of saying “I couldn’t solve this triangle,” she would be able to specifically articulate, “I was able to properly apply the law of sines, but then I forgot to take into account there could be a second answer!”
Maybe this can help too?
Sam.
Teaching low skilled freshmen, this is a daily issue for me. They are very far behind in their skill development. They have internalized their failure at (and thus, hatred of) math a long time before they get to me. Some students are much worse off than others; they are the ones who refuse to do homework, who put their heads down in class, who constantly act out, and who tend to be tardy or absent a lot. I’ve come to realize that these behaviors are due to math phobia and low self-confidence almost 100% of the time (when not due to immediate personal issues).
When I have a freshman with her head down, I crouch down quietly beside her and ask her what’s wrong. If she doesn’t immediately start crying or get mad or shut down, it’s usually not a personal or family related issue.
We discuss why he is not doing the work and it turns out he doesn’t think he can do it. I show him a problem, step by step. I wait for him to try it. Almost every time, I’ll get an “Oh, that’s all you do? That’s easy.” Or, my favorite, “Why didn’t you show us that before?” I follow this with some praise, an explicit “See, you can do math!” and a request that they try at least one or two more problems, and I get up and check on other students. Most of the time, the student will get to work and tear through the rest of their problems.
I give frequent short quizzes so they can see immediate results, and learn the message that if they work today, they will do well on the assessment tomorrow.
Now, this type of progress is highly non-linear. The student I reach today completely may be gone again next week. Students make great progress and then they slip back again, sometimes all the way back to square one. One of my favorite traditions is to write all of my students a letter at the end of the year, where I thank them, etc., and also reflect on all the progress that they have made. The grades don’t always show their true growth – which often comes in the form of now being ready to give math a chance, to believe that they can do math if they try, to come back the following year, ready to try algebra again and really mean it. The letters help give them a charge forward and they give me positive closure – even with the most difficult students.
I know that these letters are meaningful to students, because of the way they try not to look excited when I hand them out. And because, out of 80 some freshmen this year, I only found one letter left behind on the floor and none in the trash! Compare that to a typical handout… 🙂
John – I’d like to hear more about your approach that was “radical and to some extent experimental”. What did you do? I like that you approached the issue head on on day one. I’m going to try that next year.
Zac – I am surprised that this attitude is also prevalent in Singapore. For some reason I was under the impression that it was different there. Really different. Interesting. Thank you.
Sam – I found that too! They don’t know how to study math (or maths 🙂 ). Looking over notes/problems is not going to do it. Math is not a spectator sport. My suggestion to my students was to write down the problems they had already done (which we had gone over in class, so they had the correct answers) on a new, clean sheet of paper, and try them again (sans notes/book). Then go back and compare the new results with the prior work. Many of them thought I was crazy – “But I already did that problem!”
Dan – You rock. Your stories always remind me of the time I spent working at the alternative school. So many other issues with which to deal aside from the math phobia. It takes so much energy and patience. Your students are lucky to have you! I love the idea of the letter. How much time does that take?
Everyone – So, it appears this problem isn’t limited to one country. I’m guessing that we all use very different “curricula”, so that’s not it. I think it’s also safe to say that our students were taught a variety of methods before they came to our classes. I don’t think this is a “new” problem either. I remember it all too well from my own long ago high school/college days – which is part of the reason I went into teaching – to change that perception. I’ve really got to look at the survey’s from the freshmen soon – not today though. Off to do some cooking for Father’s Day!
I just did an afternoon with math teachers and integrating technology into their math classes. I introduced them to Voicethread. Here is a link to their projects. When you arrive at the Portportal, go to the Voicethread category and then WKMA (Wester Kansas math Academy). Turned out pretty good, considering they did it all in just a few hours. http://guest.portaportal.com/cyndidannerkuhn
Stumbled on this one about a year ago.
http://www.npr.org/templates/story/story.php?storyId=7406521
I try to use it two ways, this thinking about set intelligence affects both “smart” kids and those who are behind (it’s one of the reasons why GATE kids stumble in Middle/High School when it’s no long “easy”). I have to tell my son that even “genuises” make mistakes in math (his argument for the correctness of his Math homework is based on his perceived self-intelligence, and a dislike for fixing sloppy work). For low-performing students, they get stuck in the “I can’t do that rut” because it’s not easy. Giving them some successes like Dan does helps.
I hadn’t seen that article – thanks Alice. One thing I work on (especially with the freshmen), is what it means to be good at math. It is not getting the answer right the first time.
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